WASHINGTON—Hillary Clinton’s plan to deter companies from leaving the U.S. will include an “exit tax,” her campaign said Monday, making it even more restrictive than President Barack Obama’s proposals.

Like Mr. Obama, Mrs. Clinton wants to prevent companies from leaving the U.S. tax system by merging with a smaller foreign firm. That rule could have discouraged Medtronic PLC from putting its tax address in Ireland and could complicate the similar transaction that Pfizer Inc. is attempting now. Both of those deals use a law...